Lesson video

Hello, I'm Mr. Langton, and in this lesson, we're going to look at how to multiply non-unit fractions by integers.

All you're going to need is something to write with and something to write on.

Try and make sure you're in a quiet space with no distractions.

When you're ready, we'll begin.

We'll start with the try this activity.

Antoni used his diagram to calculate the first five multiples of 2/3.

Can you see we've got 2/3 there, we've got another 2/3, and that's 4/3, another 2/3 is 6/3, another 2/3 is 8/3, and another 2/3 is 10/3.

Cala looked at two lots of 2/3 and she writes down some calculations.

She starts off with two lots of 2/3 is 4/3.

Now, that also means that 2/3 multiplied by two is 4/3.

Now, if we start with 4/3 and we divide that by two, we'll get 2/3, and if we start with 4/3 and divide it by 2/3, we get two.

And all four of these calculations are linked together and they can be called the family of four.

Can you write out some similar calculations for five lots of 2/3? Have a go, pause the video.

When you're ready, we'll look at it together.

Pausing in three, two, one, go.

How did you get on? Let's write them out now.

We've got five lots of 2/3.

Five multiplied by 2/3.

That's going to be 2/3, 4/3, 6/3, 8/3, 10/3, that's five lots of it.

In case you count on your fingers, I often count on my fingers.

Five lots of 2/3 is 10/3, and that means that 2/3 multiplied by five will also be 10/3.

And it means if we start with 10/3, when we divide by 2/3, we'll get five.

And if we start with 10/3 and then we divide by five, then we're going to get 2/3.

Did you get that? Alright, let's move on to the next part.

5/12 of 60 is 25.

And we can see that from the bar model here.

We've taken 60, we've split it into 12 equal pieces, and each one of those is worth five, and 5/12 will be five lots of five, which is 25.

Yasmin has a look at that and she says, right, okay, if I have 5/12 multiplied by 60 is 25, then 60 multiplied by 5/12 is 25.

25 divided by 60 will be 5/12 and 25 divided by 5/12 equals 60.

Now, what calculations can you write for 7/12 of 60? Pause the video and have a go.

When you're done, un-pause it, and we'll go through it together.

You can pause in three, two, one, go.

Have you done it? Right, I'm going to start off now looking at 7/12.

If we know that 5/12 is on the left hand side there, then this purple bit here, I'll just highlight again, that's going to be 7/12, isn't it? 7/12 of 60 is going to be seven lots of five, which is 35.

We're going to write our family four is 7/12 of 60 makes 35, so that's 7/12 multiplied by 60 gives me 35.

I can do 60 multiplied by 7/12 to get 35.

I can do 35 divided by 12, sorry, divided by 60 even, to get 7/12.

And I can do 35 divided by 7/12 to get 60.

Okay, check your answers and then we'll move on to the next part.

Hopefully, you're now ready for the independent task.

Pause the video and access the worksheet.

When you're ready, un-pause it and we'll go through it together.

Good luck.

Right, let's see how we get on.

We'll start with the one on the top left.

Here is a diagram to show eight multiplied by 3/4 equals six.

Write a family of four for this calculation.

We've got the first one already, I won't write it again, but we've got eight times 3/4 is six, which means that 3/4 multiplied by eight will be six, and it means that six divided eight is 3/4, and six divided by 3/4 equals eight.

Right, let's go down to the next bit.

Work out the value of four lots of 2/5.

I'm going to count on my fingers again.

2/5, 4/5, 6/5, 8/5.

Great, so the family of four.

That's going to be four multiplied by 2/5 equals 8/5, and it's going to be 2/5 multiplied by four to make 8/5.

We're going to have 8/5 divided by four equals 2/5, and 8/5 divided by 2/5 equals four.

Okay so far? Right, up to the top.

Cala says that four lots of 4/5 is 16/20 and Xavier says it's 16/5.

Who is correct? Now, if we look at some of the answers that we did earlier, actually, this last one we just did, four lots of 2/5 equals 8/5.

We had 2/5 and 2/5 and 2/5 and 2/5, and we've got 8/5.

And actually, our denominator didn't change, did it, our numerator did, we have four lots of those 2/5, which means that the four lots of 4/5 is going to be 16/5.

Xavier is correct.

And that method that we used then is going to be a little bit more useful when we get down to these last four here.

Seven multiplied by 2/3 is going to be 14/3.

I would count on my fingers, but I've only got one hand available, I need to get to seven.

2/3, 4/3, 6/3, 8/3, 10/3, 12/3, 14/3.

Yes, okay.

Right, 3/4 multiplied by four, well that would be 3/4, 6/4, 9/4, 12/4.

And if you're feeling particularly clever, you'll cancel that down.

How many times does four go into 12? It goes in exactly three times.

Right, 2/3 of nine.

A couple of different ways that we could do this.

If we look at the nine lots of 2/3, we end up with 18/3.

And how many times does three go into 18, it's going to go six times.

Finally, 32 multiplied by 3/8.

This is going to be a little bit tricky and there are multiple ways we can do it.

I'm going to start off using the method we've been using all the time, we'll do 32 lots of three to get 96 over eight, and if you're snappy with your times tables, you'll know that eight goes into 96 12 times.

Now, there are other ways that you could do it.

See if we look back at the previous one, let me just change the colour, if we look back at this previous one, just here, 2/3 of nine is six, and rather than working with that numerator, we could actually start off, we could do that divided by three earlier 'cause we did 18 divided by three.

If we do the nine divided three, we get three, and we wanted two lots of that.

That's another way of getting to the six, and that actually makes this one a little bit easier.

Instead of multiplying the numerator first and then dividing to cancel it out, how many time does eight go into 32? It goes in four times.

If we do 32 divided by eight, we get four, and we need three lots of that.

Four lots of three is 12.

Two different ways that you could do those.

Okay, last activity.

I'm thinking of a number.

2/5 of my number is 14.

Can you find 5/7 of my number? If you're feeling really clever, I want you to pause it now and have a go.

If you don't quite know where to start, I'll give you a hint, just un-pause it straightaway.

If you're going to have a go right now, off you go in three, two, one.

Okay, we'll start for the hint.

I'll draw a little bar model there.

2/5 of my number is 14.

We've got this bar here represents my number.

The whole bar represents my number.

2/5 of it's 14.

Can you find 5/7 of my number? What you're going to need is another bar, which also represents my number, to try and find 5/7 of it.

Okay, what I'm going to ask you to do is pause it now, see if you can finish the question.

Pause it in three, two, one.

How'd it go? Alright, let's go through it together.

Looking at this first bar, we see that 2/5 of my number is 14, and so, 2/5 represents 14, so 2/5 represents 14, each of these individual blocks must be seven.

My number is five times seven, which is 35.

Okay, now, I've got to find 5/7 of my number, so I've got to find 5/7 of 35.

We could do that with or without the bar model.

We could try multiplying it, we could do 5/7 multiplied by 35.

You could do five lots of 35, but that's quite tricky, but we could do that division technique that I showed you earlier, could move that up to 35 divided by seven is five.

I need five lots of that.

Five lots of five is 25.

And the bar model shows that really nicely, that we're starting off with my number of 35, and we need to split it into seven equal pieces.

All the way along, this bar can split into seven pieces.

35 divided by seven is five.

Each individual block in my bar is worth five.

And I need five of those, which is 25.

5/7 of my number is 25.

Feeling good about that? Excellent, well done.